In a math class I am taking, we are discussing how to factor polynomials with grouping. For the most part, I've understood everything so far, until I was told that I needed to "Use the Distributive Law of Multiplication to factor the common polynomial out of each term".
Original: $$x^3 - 6x^2 - 3x + 18$$
In the example, after a GCF is determined as -3. At this point, factoring those out results in: $$(x^3 - 6x^2) + (-3x + 18) = x^2(x - 6) - 3(x - 6)$$
Then comes the part where it says to use the Distributive Law of Multiplication which is confusing me. This is how the example works out: $$x^2(x-6) - 3(x-6) = (x-6)(x^2-3)$$
From what I understand, distributive would mean I'd take the x squared value and multiply it by both values inside the parenthesis (x and -6) but that doesn't result in (x-6) as the example suggests. Or does it? I'm really struggling to understand what is occuring here. I've always been under the impression that the distributive property works like: $$a(b+c) = ab + ac$$
In my mind, I would simplify the above as: $$x^2(x-6) - 3(x-6)$$ $$x^3-6x^2 - 3x - 18$$
But that's not the answer :-/
Would anyone with a moment to spare care to enlighten me on how this is working?